Space of modular forms of level 5070, weight 2, and Character 5070.b

• Label: 5070.2.b
• Level: $5070$
• Weight: $2$
• Character orbit: 5070.b
• Rep. character: $\chi_{5070}(1351,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $27$
• Sturm bound: $2184$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 27 \)
Sturm bound:			\(2184\)
Trace bound:			\(22\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5070, [\chi])\).

	Total	New	Old
Modular forms	1148	100	1048
Cusp forms	1036	100	936
Eisenstein series	112	0	112

Trace form

\( 100 q + 4 q^{3} - 100 q^{4} + 100 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(5070, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5070.2.b.a	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+3iq^{7}+\cdots\)
5070.2.b.b	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+3iq^{7}+\cdots\)
5070.2.b.c	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots\)
5070.2.b.d	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots\)
5070.2.b.e	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.f	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.g	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.h	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.i	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+4iq^{7}+\cdots\)
5070.2.b.j	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.k	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+4iq^{7}+\cdots\)
5070.2.b.l	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+q^{3}-q^{4}-iq^{5}-iq^{6}+5iq^{7}+\cdots\)
5070.2.b.m	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}+2iq^{7}+\cdots\)
5070.2.b.n	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+q^{3}-q^{4}+iq^{5}-iq^{6}+2iq^{7}+\cdots\)
5070.2.b.o	$5070$	$2$	5070.b	13.b	$2$	$4$	$4$	$40.484$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}-\zeta_{12}q^{6}+\cdots\)
5070.2.b.p	$5070$	$2$	5070.b	13.b	$2$	$4$	$4$	$40.484$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{2}-q^{3}-q^{4}+\zeta_{12}q^{5}+\zeta_{12}q^{6}+\cdots\)
5070.2.b.q	$5070$	$2$	5070.b	13.b	$2$	$4$	$4$	$40.484$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{2}+q^{3}-q^{4}-\zeta_{8}q^{5}-\zeta_{8}q^{6}+\cdots\)
5070.2.b.r	$5070$	$2$	5070.b	13.b	$2$	$4$	$4$	$40.484$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
5070.2.b.s	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.t	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.u	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.v	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.w	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.x	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.y	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.z	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.ba	$5070$	$2$	5070.b	13.b	$2$	$8$	$8$	$40.484$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5070, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5070, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)